For what value of a would the following system of equations have an infinite number of solutions? 3x - 2y = 8 and 12x - 8y = 2a

a = 16

Step-by-step explanation:

A system of linear equations has an infinite number of solutions if both equations are really the same equation. Then you have only one equation, and any ordered pair on the line is a solution. Since a line has infinite length, there is an infinite number of ordered pairs that satisfies a line.

Here is the first equation.

3x - 2y = 8

Multiply both sides of the first equation by 4.

4 * 3x - 4 * 2y = 4 * 8

12x - 8y = 32

The second equation is: 12x - 8y = 2a.

The left side is now the same as the left side of the second equation.

For both equations to be the same equation, the two right sides also must be equal, so we need to have

2a = 32

Solve for a by dividing by 2.

a = 16